Man of the Match George Chigova starred in goal for Rise and Shine, who arrested a three-game losing streak with a valuable point on the road.
The result leaves Sundowns in sixth place on the League table with 14 points from eight games, while City are eight points behind in 12th spot.
The Brazilians threatened to run away with the game in the early exchanges with Khama Billiat and Wayne Arendse troubling the same post in the opening two minutes.
Chigova guided fellow Zimbabwean Billiat's chip-shot onto the upright before Arendse rose highest from the resulting corner-kick, only to see his header attempt cannon off the inside of the post.
Having survived an early onslaught from the hosts, Rise and Shine found their range through Puleng Tlolane in the 28th minute - the striker's shot from the edge of the area, well-saved by Wayne Sandilands who was handed a rare start.
Sundowns ended the half in the ascendancy with Bongani Zungu expertly losing his marker before guiding Mogakolodi Ngele's cross at goal, Chigova though was well positioned to keep the game goalless heading into the break.
The Brazilians continued to press for the opener, but were stifled in their attempts with the Rise and Shine stopper doing well to parry Hlompho Kekana's rocket away from danger on the hour.
Pitso Mosimane's men had a chance to steal all three points late on, with Katlego Mashego finding space in the box, but again Chigova came to the rescue to save at Zungu's feet.